AAA SY25 Math 7 - Practice MC 2A Add and Subtract Integers

Front

An eagle is perched on a cliff 60 feet above sea level. Below the eagle, a seagull is flying 25 feet above sea level. Further down, a fish is swimming 20 feet below sea level. Which of these statements is true?

Back

The height difference between the seagull and the eagle is 35 feet.

Answer explanation

Answer Key: -

F A. The height difference between the seagull and the eagle is -35 feet. (60 - 25 = 35) -

F B. The distance between the heights of the seagull and eagle is -35 feet. (60 - 25 = 35) -

F C. The height difference between the seagull and the fish is -45 feet. (25 - (-20) = 45) -

T D. The height difference between the seagull and the eagle is 35 feet. (60 - 25 = 35)

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M72AQ2

Front

A hawk is resting 40 feet above sea level. Below the hawk, a crow is flying 15 feet above sea level. Further down, a turtle is swimming 30 feet below sea level. Which of these statements is true?

Back

The height difference between the crow and the hawk is 25 feet.

Answer explanation

Answer Key 1:

- T A. The height difference between the crow and the hawk is 25 feet. (40 - 15 = 25)

- F B. The height difference between the crow and the hawk is -25 feet. (40 - 15 = 25)

- F C. The distance between the heights of the crow and the turtle is 45 feet. (15 - (-30) = 45)

- F D. The height difference between the crow and the turtle is -45 feet. (15 - (-30) = 45)

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M72AQ2

Front

A falcon is perched 70 feet above sea level. Below the falcon, a robin is flying 30 feet above sea level. Further down, a dolphin is swimming 15 feet below sea level. What is the height difference between the robin and the falcon?

Back

40 feet

Answer explanation

Answer Key :

- F A. The height difference between the robin and the falcon is -40 feet. (70 - 30 = 40)

- F B. The distance between the heights of the robin and the falcon is -40 feet. (70 - 30 = 40)

- T C. The height difference between the robin and the falcon is 40 feet. (70 - 30 = 40)

- F D. The height difference between the robin and the dolphin is 45 feet. (30 - (-15) = 45)

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M72AQ2

Front

A falcon is perched 70 feet above sea level. Below the falcon, a robin is flying 30 feet above sea level. Further down, a dolphin is swimming 15 feet below sea level. Which of these statements is true?

Back

The height difference between the robin and the falcon is 40 feet.

Answer explanation

Answer Key :

- F A. The height difference between the robin and the falcon is -40 feet. (70 - 30 = 40)

- F B. The distance between the heights of the robin and the falcon is -40 feet. (70 - 30 = 40)

- T C. The height difference between the robin and the falcon is 40 feet. (70 - 30 = 40)

- F D. The height difference between the robin and the dolphin is 45 feet. (30 - (-15) = 45)

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M72AQ2

Front

An osprey is sitting 55 feet above sea level. Below the osprey, a sparrow is flying 20 feet above sea level. Further down, a crab is moving 10 feet below sea level. Which of these statements is true?

Back

The height difference between the sparrow and the osprey is 35 feet.

Answer explanation

Answer Key :

- F A. The height difference between the sparrow and the osprey is -35 feet. (55 - 20 = 35)

- T B. The height difference between the sparrow and the osprey is 35 feet. (55 - 20 = 35)

- F C. The distance between the heights of the sparrow and crab is -30 feet. (20 - (-10) = 30)

- F D. The height difference between the sparrow and the crab is 30 feet. (20 - (-10) = 30)

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M72AQ2

Front

Let x = -2/3 and y = -5/6. Which expression does not have a negative value? A. x + y , B. x - y , C. y + x , D. y - x

Back

x - y

Answer explanation

Step 1: Analyze the options

We need to find which expression does not have a negative value.

A. x + y

- x + y = -2/3 + -5/6

- To add these, we need a common denominator. The LCD of 3 and 6 is 6.

- -2/3 = -4/6 and -5/6 = -5/6.

- So, -4/6 + -5/6 = -9/6 = -3/2 (which is negative).

B. x - y

- x - y = -2/3 - (-5/6)

- This becomes x - y = -2/3 + 5/6

- Convert 5/6 to 5/6, and -2/3 = -4/6,

- So, -4/6 + 5/6 = 1/6 (which is positive).

C. y + x

- This is the same as option A, x + y, so it's -9/6 = -3/2, which is negative.

D. y - x

- y - x = -5/6 - (-2/3)

- This becomes y - x = -5/6 + 2/3

- Convert -5/6 to -5/6, and 2/3 = 4/6,

- So, -5/6 + 4/6 = -1/6 (which is negative).

Final Answer:

The correct answer is:

B. x - y.

Front

Let x = -4/5 and y = -3/4. Which expression does not have a negative value? Options: x + y, x - y, y + x, y - x

Back

y - x

Answer explanation

Step 1: Analyze the options

We need to find which expression does not have a negative value.

A. x + y

- x + y = -4/5 + -3/4

- To add these, we need a common denominator. The LCD of 5 and 4 is 20.

- -4/5 = -16/20 and -3/4 = -15/20.

- So, -16/20 + -15/20 = -31/20 (which is negative).

B. x - y

- x - y = -4/5 - (-3/4)

- This becomes x - y = -4/5 + 3/4

- Convert 3/4 to 15/20, and -4/5 = -16/20,

- So, -16/20 + 15/20 = -1/20 (which is negative).

C. y + x

- This is the same as option A, x + y, so it's -31/20, which is negative.

D. y - x

- y - x = -3/4 - (-4/5)

- This becomes y - x = -3/4 + 4/5

- Convert -3/4 to -15/20, and 4/5 = 16/20,

- So, -15/20 + 16/20 = 1/20 (which is positive).

Final Answer:

The correct answer is:

D. y - x.

Front

Let x = -7/10 and y = -5/6. Which expression does not have a negative value? A. x - y , B. x + y, C. y + x, D. y - x

Back

x - y

Answer explanation

Step 1: Analyze the options

We need to find which expression does not have a negative value.

A. x - y

- x - y = -7/10 - (-5/6)

- This becomes x - y = -7/10 + 5/6

- Convert 5/6 to 15/30, and -7/10 = -21/30,

- So, -21/30 + 15/30 = -6/30 = -1/5 (which is negative).

B. x + y

- x + y = -7/10 + -5/6

- To add these, we need a common denominator. The LCD of 10 and 6 is 30.

- -7/10 = -21/30 and -5/6 = -25/30.

- So, -21/30 + -25/30 = -46/30 = -23/15 (which is negative).

C. y + x

- This is the same as option B, x + y, so it's -46/30 = -23/15, which is negative.

D. y - x

- y - x = -5/6 - (-7/10)

- This becomes y - x = -5/6 + 7/10

- Convert -5/6 to -25/30, and 7/10 = 21/30,

- So, -25/30 + 21/30 = -4/30 = -2/15 (which is negative).

Final Answer:

The correct answer is:

A. x - y.

Front

Jamie wants to place a bookshelf in the center of a wall that is 13 1/2 feet wide. The bookshelf is 3 1/4 feet wide. How many feet from each side of the wall must the bookshelf be so that it is centered?

Back

5 1/8 feet

Answer explanation

Answer:

To solve this problem, we need to figure out how far the bookshelf is from each side of the wall when it's centered. Let’s break it down step by step:

Step 1: Total width of the wall

The wall is 13 1/2 feet wide. Let’s convert this mixed number into an improper fraction:

13 1/2 = (26/2) + (1/2) = 27/2

Step 2: Width of the bookshelf

The bookshelf is 3 1/4 feet wide. Convert this to an improper fraction:

3 1/4 = (12/4) + (1/4) = 13/4

Step 3: Remaining space on the wall

To find out how much space is left on the wall (not covered by the bookshelf), subtract the bookshelf’s width from the total wall width:

27/2 − 13/4

To subtract, we need a common denominator. The least common denominator of 2 and 4 is 4:

27/2 = 54/4

Now subtract:

54/4 − 13/4 = 41/4

Step 4: Divide the remaining space into two equal parts

The remaining space is on both sides of the bookshelf, so divide it by 2 to find out how much is on each side:

(41/4) ÷ 2 = (41/4) × (1/2) = 41/8

Simplify and convert to a mixed number:

41/8 = 5 1/8

Final Answer: The bookshelf must be 5 1/8 feet from each side of the wall.

Correct Option: C

Front

Wall width: 15 2/5 feet, Painting width: 3 3/10 feet. How many feet from each side of the wall must the painting be to be centered?

Back

5 9/10 feet

Answer explanation

Answer:

To solve this problem, we need to figure out how far the painting is from each side of the wall when it's centered. Let’s break it down step by step:

Step 1: Total width of the wall

The wall is 15 2/5 feet wide. Let’s convert this mixed number into an improper fraction:

15 2/5 = (75/5) + (2/5) = 77/5

Step 2: Width of the painting

The painting is 3 3/10 feet wide. Convert this to an improper fraction:

3 3/10 = (30/10) + (3/10) = 33/10

Step 3: Remaining space on the wall

To find out how much space is left on the wall (not covered by the painting), subtract the painting’s width from the total wall width:

77/5 − 33/10

To subtract, we need a common denominator. The least common denominator of 5 and 10 is 10:

77/5 = 154/10

Now subtract:

154/10 − 33/10 = 121/10

Step 4: Divide the remaining space into two equal parts

The remaining space is on both sides of the painting, so divide it by 2 to find out how much is on each side:

(121/10) ÷ 2 = (121/10) × (1/2) = 121/20

Simplify and convert to a mixed number:

121/20 = 6 1/20

Final Answer: The painting must be 6 1/20 feet from each side of the wall.

Correct Option: D